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Helical milling is an advanced hole-making process and different approaches considering controllable variables have been presented addressing modeling and optimization of machining forces in helical milling. None of them considers the importance of the noise variables and the fact that machining forces components are usually correlated. Exploring this issue, this paper presents a multivariate robust modeling and optimization of cutting forces of the helical milling of the aluminum alloy Al 7075. For the study, the tool overhang length was defined as noise variable since in cavities machining, there are specific workpiece geometries that constrain this variable; the controllable variables were axial feed per tooth, tangential feed per tooth, and cutting speed. The cutting forces in the workpiece coordinate system were measured and the components in the tool coordinate system, i.e., the axial and radial forces, were evaluated. Since these two outcomes are correlated, the weighted principal component analysis was performed together with the robust parameter design to allow the multivariate robust modeling of the mean and variance equations. The normal boundary intersection method was used to obtain a set of Pareto robust optimal solutions related to the mean and variance equations of the weighted principal component. The optimization of the weighted principal component through the normal boundary intersection method was performed and the results evaluated in the axial and radial cutting force components. Confirmation runs were carried out and it was possible to conclude that the models presented good fit with experimental data and that the Pareto optimal point chosen for performing the confirmation runs is robust to the tool overhang length variation. Finally, the cutting force models were also presented for mean and variance in the workpiece coordinate system in the time domain, presenting low error regarding the experimental test, endorsing the results. [ABSTRACT FROM AUTHOR]

In practical situations, solving a given problem usually calls for the systematic and simultaneous analysis of more than one objective function. Hence, a worthwhile research question may be posed thus: In multiobjective optimization, what can facilitate for the decision maker choosing the best weighting? Thus, this study attempts to propose a method that can identify the optimal weights involved in a multiobjective formulation. The proposed method uses functions of Entropy and Global Percentage Error as selection criteria of optimal weights. To demonstrate its applicability, this method was employed to optimize the machining process for vertical turning, maximizing the productivity and the life of cutting tool, and minimizing the cost, using as the decision variables feed rate and rotation of the cutting tool. The proposed optimization goals were achieved with feed rate = 0.37 mm/rev and rotation = 250 rpm. Thus, the main contributions of this study are the proposal of a structured method, differentiated in relation to the techniques found in the literature, of identifying optimal weights for multiobjective problems and the possibility of viewing the optimal result on the Pareto frontier of the problem. This viewing possibility is very relevant information for the more efficient management of processes. [ABSTRACT FROM AUTHOR]

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A mixed ceramic is a type of cutting-tool material widely employed for machining hardened steels. The usage of a mixed ceramic along with a wiper geometry can help double the feed rate, thereby increasing productivity while keeping the surface roughness ( Ra ) as low as possible. Analyses of manufacturing processes, such as a machining process, show that the various possible controlled parameters can be modeled by multiobjective mathematical models to ensure their optimization. Hence, the aim of this study was optimize a hard turning process using a robust weighting based on diversity to choose the final Pareto optimal solution of the multiobjective problem. The responses of the material removal rate ( MRR ), Ra parameter, and cutting force ( Fc ) were modeled by using the response surface methodology; in this methodology, decision variables, such as the cutting speed ( Vc ), feed rate ( f ), and depth of cut ( d ), are employed. The diversity index, as a decision-making criterion, proved to be useful in mapping the regions of minimum variance within the Pareto optimal responses obtained in the optimization process. Hence, the study demonstrates that the weights used in the multiobjective optimization process influence the prediction variance of the obtained response. [ABSTRACT FROM AUTHOR]